CN108646564A - A kind of design method of the uncertain reentry vehicle model based on event triggering - Google Patents
A kind of design method of the uncertain reentry vehicle model based on event triggering Download PDFInfo
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Abstract
The invention discloses a kind of design method of the uncertain reentry vehicle model based on event triggering, this method includes：Step 1：It establishes and does not know re-entry vehicle system model, and design point observer and output feedback controller, constitute closed-loop control system；Step 2：Lyapunov functions are defined, trigger conditions are designed based on this Lyapunov function；Step 3：Indeterminate is eliminated, scaling is carried out by trigger conditions, the stability of closed-loop control system is proved using linear matrix inequality technology.The present invention is based on the design methods of the uncertain reentry vehicle model of event triggering to reduce the unnecessary waste of system resource while ensureing that re-entry vehicle system is stablized, achieve higher resource utilization.
Description
Technical field
The present invention relates to flying vehicles control technical field more particularly to a kind of uncertain ablated configurations based on event triggering
The design method of device model.
Background technology
The Guidance and control technology of reentry vehicle is the focus of various countries' aircraft research field, reentry vehicle all the time
Flying method be different from other aircrafts, need to carry through other carriers and then be again introduced into atmosphere, therefore this aircraft
Flying speed with superelevation can be realized and reach the whole world anywhere in one hour.Process is reentered in reentry vehicle
In, the flight time is elongated, flight environment of vehicle constantly changes and the various factors such as centroid motion can influence the stability of system, so
Accurately controlling for the aircraft of this hypersonic is particularly important.
Event trigger mechanism is proposed to overcome the waste unnecessary to calculating and the communication resource of time sampling mechanism
, it is put into the research of event trigger mechanism there are many scholar later, net is efficiently used primarily directed to network control system
Network resource reduces this angle of the utilization of resources to study.Event trigger mechanism is only needed in a certain preset event item
Part just carries out sampling transmission when occurring, and the performance of control system is similar to the system performance under time triggered.Pass through selection
Suitable event condition, event trigger mechanism significantly reduce sampled point, to effectively save network bandwidth resources.It is right
It is fed back in output, output is fed back to the partial feedback of system structure information, but always measurable due to exporting, so output is anti-
Feedback is always physically achievable, and it is low to export feedback economic cost in engineer application.
Number of patent application is：201710198546.6 a kind of adoption status feedback is compound with the hypersonic vehicle of neural network
Control method first designs large gain STATE FEEDBACK CONTROL by measuring the angle of attack, the rate of pitch signal of hypersonic aircraft
Device is directed to the strong uncertainty of hypersonic aircraft aerodynamic parameter on this basis, uses one kind using SIN function as base
The neural network structure of function devises the adaptive updating rule of neural network weight, finally forms hypersonic aircraft
The composite controller of neural network and feedback of status realizes the tracking to it is expected angle of attack signal.The patent has the disadvantages that：
(1) feedback of status generally physically can not achieve, or even if can realize but economic cost is very high, thus physical constraint make it is defeated
Go out feedback more often to use.(2) do not consider that the immesurable situation of system mode, use state observer can solve the problems, such as this.
Number of patent application is：201611100078.6 a kind of extension robust H based on control constraints∞Unmanned aerial vehicle (UAV) control side
Method, the method for the invention obtain the MATRIX INEQUALITIES that controller need to meet when controlled quentity controlled variable exists and constrains, additionally it is possible to determine most
Controlled quentity controlled variable is specifically constrained in the case of big interference, and in order to improve controller under conditions of meeting constraint
Performance also extends state variable.The patent has the disadvantages that：(1) event trigger mechanism is not considered, can increase data transmission
Pressure wastes network bandwidth resources.(2) do not consider therefore the influence of uncertain factor, the stability of system can be affected.
Invention content
The technical problem to be solved of the present invention is that prior art re-entry vehicle system causes system resource not
Necessary waste, the low defect of resource utilization provide a kind of uncertain reentry vehicle model triggered based on event
Design method.
The present invention is achieved by the following technical solutions：A kind of uncertain reentry vehicle model based on event triggering
Design method, this method includes：
Step 1：It establishes and does not know re-entry vehicle system model, and design point observer and output feedback controller,
Constitute closed-loop control system；
Step 2：Lyapunov functions are defined, trigger conditions are designed based on this Lyapunov function；
Step 3：Indeterminate is eliminated, scaling is carried out by trigger conditions, is demonstrate,proved using linear matrix inequality technology
The stability of bright closed-loop control system.
One of preferred embodiment as the present invention, establishes the specific mistake for not knowing reentry vehicle model in the step 1
Cheng Wei：
Initially set up reentry vehicle model：
Q=0.5 ρ1v2, ρ1=ρ0e-ξh,
In formula：M, v are respectively the quality and speed of aircraft；ωx, ωy, ωzRespectively body x-axis, y-axis, the angle of z-axis
Speed；T, FT, FNIt is axis to the air force of barycenter；Mx, My, MzRespectively x-axis, y-axis, the torque of z-axis；γ, ψ are respectively
Flight-path angle and course angle；R is earth radius；θ,Respectively longitude and latitude；ξ is the inclination angle of reentry vehicle；Ix, Iy,
Iz, Ixy, Iyz, IzxIndicate the rotary inertia of axis；R is height of the barycenter relative to the earth's core；Q is dynamic pressure；ρ1For air
Density, ρ0For sea-level atmosphere layer density；X, z are horizontal, lateral distance；CD, CLRespectively resistance, lift coefficient；S is flight
Device area of reference；ωe, g0Respectively earth rate and acceleration of gravity；ξ, h are respectively bulkfactor and height above sea level；By
After first-order linear, above-mentioned equation is represented by
Wherein,For the state vector of controlled device；U (t)=(α β ξ δeδaδr
)TFor the input vector of controlled device；α、β、ξ、δe、δaAnd δrThe respectively angle of attack of reentry vehicle, yaw angle, inclination angle, liter
The deflection of rudder, aileron and rudder drops；A and B is respectively sytem matrix and input matrix；
Secondly, indeterminate factor is added and obtains uncertain reentry vehicle model：Process is reentered in reentry vehicle
In, system can be influenced by uncertain factor and be changed, therefore the stability of system can also be affected；So this
Invention considers the reentry vehicle model containing indeterminate.
Wherein, x (t) ∈ Rn×1For the state vector of controlled device；u(t)∈Rm×1For the input vector of controlled device；y
(t)∈Rq×1For the output vector of controlled device；A, B, C are respectively sytem matrix, input matrix, output matrix；Δ A be A not
It determines item, and meets Δ A=DF (t) E, D, E are known permanent matrix, and F (t) meets FT(t)F(t)≤I；Assuming that (A, C) can
It sees, (A, B) is controllable.
One of preferred embodiment as the present invention, since the state variable in real system not can be directly acquired all,
In order to estimate that unknown virtual condition, the design point observer are as follows：
Wherein,For the state vector of state observer,The output of micro- state observer to
Amount, L ∈ Rn×qFor the gain matrix of state observer；
According to state observer, the design output feedback controller is as follows：
Wherein, K ∈ Rm×nFor feedback gain matrix to be determined.
One of preferred embodiment as the present invention, in the step 2：The trigger conditions are with one about State Viewpoint
Survey the inequality description of device output variable；Trigger conditions event built in event detection device, event detection device continuously from
The information for receiving output variable at sensor, when meeting trigger conditions, ability talent believes the output at this moment sampled
Breath passes to output feedback controller, this moment is referred to as that triggering moment is denoted as tk；Due to the effect of zero-order holder, next
A triggering moment tk+1Before arrival, output feedback controller is always maintained at the information of a triggering moment.
One of preferred embodiment as the present invention, the output feedback controller based on event trigger mechanism is only in tkThis
A moment update, wherein tkIndicate k-th of sampling period corresponding triggering moment：
Define output error：
Wherein,It is current sampled signal,It is the event detection device last time to send output feedback ontrol to
The sampled signal of device, due to the effect of zero-order holder, in next triggering moment tk+1Before arrival, output feedback controller
It is always maintained at the information of a triggering moment；
Definition status evaluated error vector is：
Then state estimation error equation is：
Defining trigger conditions is：
Wherein, σ ＞ 0.When formula (9) is unsatisfactory for, then the sampled value at current time is recorded, and is transferred to output feedback
Controller, update output feedback controller input.
Then, we can obtain new closed-loop system expression formula：
Defining Lyapunov functions is：
Wherein, P1、P2、P3Respectively positive definite matrix.
One of preferred embodiment as the present invention, the detailed process of the step 3 is：It is demonstrate,proved by Liapunov's direct method
The stability of bright system, that is, ensureBut, it needs to eliminate indeterminate Δ during proof system stability
A can eliminate indeterminate Δ A by following lemma, and lemma can be described as：
If x (t) ∈ Rn×1, y (t) ∈ Rq×1, ε ＞ 0, D and E are respectively the real number matrix of known suitable dimension, and F (t) is
Unknown matrix and it is satisfied with FT(t) F (t)≤I, wherein I are unit matrixs, then
2xT(t)DF(t)Ey(t)≤εxT(t)DDTx(t)+ε-1yT(t)ETEy(t)； (12)
After eliminating indeterminate Δ A by this lemma, the stability of proof system need to be continued；To ensure that system is stablized,Scaling can be carried out by trigger conditions, a linear matrix inequality Solve problems, inequality can be converted into later
For：
When obtaining system parameters, suitable P is solved1, P2, P3, σ meets this linear matrix inequality i.e. system
Lyapunov stablizes.
The present invention compared with prior art the advantages of be：The present invention is based on the uncertain reentry vehicle models of event triggering
Design method, ensure re-entry vehicle system stablize while, reduce the unnecessary waste of system resource, achieve more
High resource utilization.
Description of the drawings
Fig. 1 is the control algolithm flow chart of the present invention；
Fig. 2 is structure chart of the reentry vehicle based on event trigger mechanism of the present invention.
Specific implementation mode
It elaborates below to the embodiment of the present invention, the present embodiment is carried out lower based on the technical solution of the present invention
Implement, gives detailed embodiment and specific operating process, but protection scope of the present invention is not limited to following implementation
Example.
As shown in Figs. 1-2：A kind of design method of the uncertain reentry vehicle model based on event triggering, this method packet
It includes：
Step 1：It establishes and does not know re-entry vehicle system model, and design point observer and output feedback controller,
Constitute closed-loop control system；
It establishes and does not know the detailed process of reentry vehicle model and be：
Initially set up reentry vehicle model：
Q=0.5 ρ1v2, ρ1=ρ0e-ξh,
In formula：M, v are respectively the quality and speed of aircraft；ωx, ωy, ωzRespectively body x-axis, y-axis, the angle of z-axis
Speed；T, FT, FNIt is axis to the air force of barycenter；Mx, My, MzRespectively x-axis, y-axis, the torque of z-axis；γ, ψ are respectively
Flight-path angle and course angle；R is earth radius；θ,Respectively longitude and latitude；ξ is the inclination angle of reentry vehicle；Ix, Iy,
Iz, Ixy, Iyz, IzxIndicate the rotary inertia of axis；R is height of the barycenter relative to the earth's core；Q is dynamic pressure；ρ1For air
Density, ρ0For sea-level atmosphere layer density；X, z are horizontal, lateral distance；CD, CLRespectively resistance, lift coefficient；S is flight
Device area of reference；ωe, g0Respectively earth rate and acceleration of gravity；ξ, h are respectively bulkfactor and height above sea level；By
After first-order linear, above-mentioned equation is represented by
Wherein,For the state vector of controlled device；U (t)=(α β ξ δeδaδr
)TFor the input vector of controlled device；α、β、ξ、δe、δaAnd δrThe respectively angle of attack of reentry vehicle, yaw angle, inclination angle, liter
The deflection of rudder, aileron and rudder drops；A and B is respectively sytem matrix and input matrix；
Secondly, indeterminate factor is added and obtains uncertain reentry vehicle model：Process is reentered in reentry vehicle
In, system can be influenced by uncertain factor and be changed, therefore the stability of system can also be affected；So this
Invention considers the reentry vehicle model containing indeterminate.
Wherein, x (t) ∈ Rn×1For the state vector of controlled device；u(t)∈Rm×1For the input vector of controlled device；y
(t)∈Rq×1For the output vector of controlled device；A, B, C are respectively sytem matrix, input matrix, output matrix；Δ A be A not
It determines item, and meets Δ A=DF (t) E, D, E are known permanent matrix, and F (t) meets FT(t)F(t)≤I；Assuming that (A, C) can
It sees, (A, B) is controllable；
Since the state variable in real system not can be directly acquired all, in order to estimate unknown virtual condition, institute
It is as follows to state design point observer：
Wherein,For the state vector of state observer,The output of micro- state observer to
Amount, L ∈ Rn×qFor the gain matrix of state observer；
According to state observer, the design output feedback controller is as follows：
Wherein, K ∈ Rm×nFor feedback gain matrix to be determined；
Step 2：Lyapunov functions are defined, trigger conditions are designed based on this Lyapunov function；
Trigger conditions are described with an inequality about state observer output variable；Built in event detection device
Trigger conditions event, event detection device continuously receive the information of output variable from sensor, are triggered when meeting event
The output information at this moment sampled is passed to output feedback controller by ability talent when condition, when this moment is referred to as triggering
It engraves as tk；Due to the effect of zero-order holder, in next triggering moment tk+1Before arrival, output feedback controller is always
Keep the information of a triggering moment；
The output feedback controller based on event trigger mechanism is only in tkThis moment updates, wherein tkIt indicates k-th
Sampling period corresponding triggering moment：
Define output error：
Wherein,It is current sampled signal,It is the event detection device last time to send output feedback ontrol to
The sampled signal of device, due to the effect of zero-order holder, in next triggering moment tk+1Before arrival, output feedback controller
It is always maintained at the information of a triggering moment；
Definition status evaluated error vector is：
Then state estimation error equation is：
Defining trigger conditions is：
Wherein, σ ＞ 0；When formula (9) is unsatisfactory for, then the sampled value at current time is recorded, and is transferred to output feedback
Controller, update output feedback controller input.
Then, we can obtain new closed-loop system expression formula：
Defining Lyapunov functions is：
Wherein, P1、P2、P3Respectively positive definite matrix；
Step 3：Indeterminate is eliminated, scaling is carried out by trigger conditions, is demonstrate,proved using linear matrix inequality technology
The stability of bright closed-loop control system；Detailed process is：By the stability of Liapunov's direct method proof system, that is, ensureBut, need cancellation indeterminate Δ A that can be eliminated not by following lemma during proof system stability
Determine that item Δ A, lemma can be described as：
If x (t) ∈ Rn×1, y (t) ∈ Rq×1, ε ＞ 0, D and E are respectively the real number matrix of known suitable dimension, and F (t) is
Unknown matrix and it is satisfied with FT(t) F (t)≤I, wherein I are unit matrixs, then
2xT(t)DF(t)Ey(t)≤εxT(t)DDTx(t)+ε-1yT(t)ETEy(t)； (12)
After eliminating indeterminate Δ A by this lemma, the stability of proof system need to be continued；To ensure that system is stablized,Scaling can be carried out by trigger conditions, a linear matrix inequality Solve problems, inequality can be converted into later
For：
When obtaining system parameters, suitable P is solved1, P2, P3, σ meets this linear matrix inequality i.e. system
Lyapunov stablizes.
Referring to Fig. 1：Below in conjunction with example given above, the control algolithm of the present invention is sketched：
(1) in the example, it is contemplated that reentry vehicle model, is arranged algorithm parameter and each matrix data of system；
(2) node initializing obtains original stateIt is exported againNumerical value, calculate output errorCarry out following judgement and operation：When inequality (9) are set up, then to outputNonuniform sampling is carried out, is obtained
Event triggering sampling outputIf inequality (9) is invalid, continue to calculate (9), just starts to sample when setting up；
(3) by the event triggering sampling output obtained by step (2)It is defeated to be updated to designed output feedback controller
Enter formula (5) to calculate and update control input u (t)；
(4) continue to update system outputAnd errorReturn to step 2, continuation are carried out according to above-mentioned steps.
Below to system stability into line justification：
Take Lyapunov functions
Wherein P1、P2、P3Respectively positive definite matrix can be solved by inequality (13) and be obtained.To Lyapunov functions along closing
The track derivation of loop system (10), has
The formula 2x containing indeterminate occurred in above formulaT(t)P1Δ Ax (t) andIt can be by front
The lemma mentioned eliminates indeterminate Δ A, and detailed process is：
With
Consider trigger conditionsIt is rightScaling is carried out, can be obtained
When ensureing that inequality (13) is set up, you can ensureTrigger conditions (9) be it is feasible, can be with
Ensure that closed-loop system is stable.
The present invention is based on the design methods of the uncertain reentry vehicle model of event triggering, are ensureing reentry vehicle system
While system is stablized, reduces the unnecessary waste of system resource, achieve higher resource utilization.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement etc., should all be included in the protection scope of the present invention made by within refreshing and principle.
Claims (6)
1. a kind of design method of the uncertain reentry vehicle model based on event triggering, which is characterized in that this method includes：
Step 1：It establishes and does not know re-entry vehicle system model, and design point observer and output feedback controller, constitute
Closed-loop control system；
Step 2：Lyapunov functions are defined, trigger conditions are designed based on this Lyapunov function；
Step 3：Indeterminate is eliminated, scaling is carried out by trigger conditions, is closed using linear matrix inequality technology proof
The stability of ring control system.
2. the design method of the uncertain reentry vehicle model according to claim 1 based on event triggering, feature
It is, the detailed process that uncertain reentry vehicle model is established in the step 1 is：
Initially set up reentry vehicle model：
In formula：M, v are respectively the quality and speed of aircraft；ωx, ωy, ωzRespectively body x-axis, y-axis, the angular speed of z-axis；
T, FT, FNIt is axis to the air force of barycenter；Mx, My, MzRespectively x-axis, y-axis, the torque of z-axis；γ, ψ are respectively flight path
Angle and course angle；R is earth radius；θ,Respectively longitude and latitude；ξ is the inclination angle of reentry vehicle；Ix, Iy, Iz, Ixy,
Iyz, IzxIndicate the rotary inertia of axis；R is height of the barycenter relative to the earth's core；Q is dynamic pressure；ρ1For atmospheric density, ρ0
For sea-level atmosphere layer density；X, z are horizontal, lateral distance；CD, CLRespectively resistance, lift coefficient；S is the aircraft plane of reference
Product；ωe, g0Respectively earth rate and acceleration of gravity；ξ, h are respectively bulkfactor and height above sea level；By first-order linear
After change, above-mentioned equation is represented by
Wherein,For the state vector of controlled device；U (t)=(α β ξ δeδaδr)TFor quilt
Control the input vector of object；α、β、ξ、δe、δaAnd δrThe respectively angle of attack of reentry vehicle, yaw angle, inclination angle, elevator, pair
The deflection of the wing and rudder；A and B is respectively sytem matrix and input matrix；
Secondly, indeterminate factor is added and obtains uncertain reentry vehicle model：
Wherein, x (t) ∈ Rn×1For the state vector of controlled device；u(t)∈Rm×1For the input vector of controlled device；y(t)∈Rq ×1For the output vector of controlled device；A, B, C are respectively sytem matrix, input matrix, output matrix；Δ A is the uncertain of A
, and meeting Δ A=DF (t) E, D, E are known permanent matrix, and F (t) meets FT(t)F(t)≤I；Assuming that (A, C) is considerable,
(A, B) is controllable.
3. the design method of the uncertain reentry vehicle model according to claim 1 based on event triggering, feature
It is, the design point observer is as follows：
Wherein,For the state vector of state observer,The output vector of micro- state observer, L ∈
Rn×qFor the gain matrix of state observer；
According to state observer, the design output feedback controller is as follows：
Wherein, K ∈ Rm×nFor feedback gain matrix to be determined.
4. the design method of the uncertain reentry vehicle model according to claim 1 based on event triggering, feature
It is, in the step 2：The trigger conditions are described with an inequality about state observer output variable；Thing
Trigger conditions event built in part detection device, event detection device continuously receive the information of output variable from sensor,
When meeting trigger conditions, the output information at this moment sampled is passed to output feedback controller by ability talent, claims this
One moment was that triggering moment is denoted as tk；Due to the effect of zero-order holder, in next triggering moment tk+1Before arrival, output
Feedback controller is always maintained at the information of a triggering moment.
5. the design method of the uncertain reentry vehicle model according to claim 4 based on event triggering, feature
It is, the output feedback controller based on event trigger mechanism is only in tkThis moment updates, wherein tkIt indicates to adopt for k-th
Sample period corresponding triggering moment：
Define output error：
Wherein,It is current sampled signal,It is the event detection device last time to send output feedback controller to
Sampled signal, due to the effect of zero-order holder, in next triggering moment tk+1Before arrival, output feedback controller is always
Keep the information of a triggering moment；
Definition status evaluated error vector is：
Then state estimation error equation is：
Defining trigger conditions is：
Wherein, σ ＞ 0.When formula (9) is unsatisfactory for, then the sampled value at current time is recorded, and be transferred to output feedback ontrol
Device, update output feedback controller input.
Then, we can obtain new closed-loop system expression formula：
Defining Lyapunov functions is：
Wherein, P1、P2、P3Respectively positive definite matrix.
6. the design method of the uncertain reentry vehicle model according to claim 1 based on event triggering, feature
It is, the detailed process of the step 3 is：By the stability of Liapunov's direct method proof system, that is, ensureBut, need cancellation indeterminate Δ A that can be eliminated not by following lemma during proof system stability
Determine that item Δ A, lemma can be described as：
If x (t) ∈ Rn×1, y (t) ∈ Rq×1, the real number matrix of ε ＞ 0, D and the respectively known suitable dimensions of E, F (t) is unknown
Matrix and it is satisfied with FT(t) F (t)≤I, wherein I are unit matrixs, then
2xT(t)DF(t)Ey(t)≤εxT(t)DDTx(t)+ε-1yT(t)ETEy(t)； (12)
After eliminating indeterminate Δ A by this lemma, the stability of proof system need to be continued；To ensure that system is stablized,
Scaling can be carried out by trigger conditions, a linear matrix inequality Solve problems can be converted into later, inequality is：
When obtaining system parameters, suitable P is solved1, P2, P3, σ meets this linear matrix inequality i.e. system
Lyapunov stablizes.
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| CN109976361A (en) * | 2019-03-14 | 2019-07-05 | 天津大学 | Quadrotor drone attitude control method towards event triggering |
| CN110456821A (en) * | 2019-08-22 | 2019-11-15 | 安徽大学 | Aerial vehicle trajectory method for optimally controlling and system based on Dynamic trigger mechanism |
| CN111487866A (en) * | 2020-04-09 | 2020-08-04 | 中北大学 | Hypersonic aircraft nerve anti-interference control method based on mixed event trigger mechanism |
| CN112180717A (en) * | 2020-10-14 | 2021-01-05 | 河北工业大学 | Heat exchanger temperature fuzzy control method and system based on 2D model |
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